課程名稱 |
微積分3 CALCULUS (3) |
開課學期 |
110-2 |
授課對象 |
地理環境資源學系 |
授課教師 |
蔡雅如 |
課號 |
MATH4008 |
課程識別碼 |
201 49830 |
班次 |
14 |
學分 |
2.0 |
全/半年 |
半年 |
必/選修 |
必修 |
上課時間 |
第1,2,3,4,5,6,7,8 週 星期二1,2(8:10~10:00)星期四3,4,10(10:20~18:20) |
上課地點 |
共201共201 |
備註 |
本課程中文授課,使用英文教科書。密集課程。統一教學,四10為實習課,期考於周末舉辦 限本系所學生(含輔系、雙修生) 總人數上限:180人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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課程概述 |
這是一門半學期的課程,主要介紹多變數函數的微積分運算,和其在經濟學豐富的應用。
微分主題包含多變數函數的極限,偏微分,方向導數,切平面,線性逼近,和微分連鎖律;並討論求函數極值,Lagrange乘子法等應用問題。積分部分涵蓋多重積分與逐次積分的定義,Fubini定理,和變數變換;並探究機率如何使用重積分。最後,課程將簡介級數與泰勒展式,解釋如何以多項式逼近複雜的函數。
課堂上將講解定義並推導重要定理,以培養學生邏輯推理與分析能力;同時會示範微積分在各領域的應用,幫助學生將微積分與其他專業科目結合。本課程還設有習題課,學生將在助教的帶領下熟練微積分的計算。
Calculus of multivariable functions together with its profound applications in Economics are introduced in this half-semester course. Especially, topics about differentiation include limits, partial derivatives, directional derivatives, tangent planes, linear approximations, and the chain rule. Also, applications such as finding extreme values and methods of Lagrange multipliers are discussed. Topics about integration involve definitions of multiple integrals and iterated integrals, Fubini’s theorem, change of variables, and how multiple integrals are used in probability. In addition to these, series and Taylor expansions are briefly introduced in the end of this course to explain how complicated functions are approximated by polynomials.
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sessions in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants. |
課程目標 |
修完本課程學生能熟悉微積分工具,並應用在各學科。
Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. |
課程要求 |
學生需要具備「微積分1」、「微積分2」的基礎。學生應積極參與課堂和習題課的活動與討論。
Students should have taken Calculus 1 and Calculus 2 before they participate in this course. They are expected to attend and participate actively in lectures as well as discussion sessions. |
預期每週課後學習時數 |
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Office Hours |
每週二 11:00~12:20 每週一 15:40~17:00 備註: 老師辦公室: 天數館 528 (Astro-Math building room 528) |
指定閱讀 |
Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early
Transcendentals, 9th edition.
NTU COOL 課程網站:
其他相關資訊
微積分甲統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html
台大微甲考古題 http://www.math.ntu.edu.tw/~calc/cp_n_34456.html
數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator
免費知識型計算引擎: https://www.wolframalpha.com |
參考書目 |
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
期考 Final Exam |
40% |
4/9 (Sat) 14:00-16:30 |
2. |
小考 Quizzes |
35% |
3/3, 3/17, 3/31 17:30-18:20 |
3. |
作業 Homework |
25% |
There are weekly WeBWorK homework and exercises (紙本作業)。There are also 3 worksheets. |
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